Question
A tank is 7 metre long and 4 meter wide wide. At what speed should water run through a pipe 5 cm broad and 4 cm deep so that in 6 hours and 18 minutes water level in the tank rises by 4.5 meter?
Answer: Option A
Rate of flow of water = x cm/minute
∴ Volume of water that flowed in the in 1 minutes
= (5 × 4 × x) = 20 x cu.cm.
∴ Volume of water that flowed in the tank in 6 hours 18 minutes.
i.e. (6 × 60 + 18) = 378 minutes
= 2x × 378 cu. cm.
According to question,
$$\eqalign{
& {\text{20}}x \times 378 = 700 \times 400 \times 450 \cr
& \Rightarrow x = \left( {\frac{{700 \times 400 \times 450}}{{20 \times 378}}} \right){\text{cm /minutes}} \cr
& \Rightarrow x = \left( {\frac{{700 \times 400 \times 450 \times 60}}{{100000 \times 20 \times 378}}} \right){\text{km/hours}} \cr
& \Rightarrow x{\text{ = 10 km/hours}} \cr} $$
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Rate of flow of water = x cm/minute
∴ Volume of water that flowed in the in 1 minutes
= (5 × 4 × x) = 20 x cu.cm.
∴ Volume of water that flowed in the tank in 6 hours 18 minutes.
i.e. (6 × 60 + 18) = 378 minutes
= 2x × 378 cu. cm.
According to question,
$$\eqalign{
& {\text{20}}x \times 378 = 700 \times 400 \times 450 \cr
& \Rightarrow x = \left( {\frac{{700 \times 400 \times 450}}{{20 \times 378}}} \right){\text{cm /minutes}} \cr
& \Rightarrow x = \left( {\frac{{700 \times 400 \times 450 \times 60}}{{100000 \times 20 \times 378}}} \right){\text{km/hours}} \cr
& \Rightarrow x{\text{ = 10 km/hours}} \cr} $$
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